INTENDED AUDIENCE :1st year B.Tech, Mathematics HonoursPREREQUISITES : Grade XIIINDUSTRIES SUPPORT :None
Basic Calculus 1 and 2
Indian Institute of Technology Kanpur and NPTEL via Swayam
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Overview
Topics of continuity, differentablity, integrability of a real valued function will be discussed with their applications. Also series representations of some functions will be discussed.
INTENDED AUDIENCE :1st year B.Tech, Mathematics HonoursPREREQUISITES : Grade XIIINDUSTRIES SUPPORT :None
INTENDED AUDIENCE :1st year B.Tech, Mathematics HonoursPREREQUISITES : Grade XIIINDUSTRIES SUPPORT :None
Syllabus
COURSE LAYOUT
Week 1:Algebra of Real Numbers, set of Axioms,Completeness,Density, decimal representation of real numbersWeek 2:Convergence of sequences, properties of limit, Sandwich Theorem, Monotonic sequences, Cantor's completeness Principle, Bolzano-Weierstrass Theorem, Cauchy's completenessWeek 3:Convergence of series, comparison test, Root test, Ratio test ,Power series, Leibniz's conditionWeek 4:Continuity, Intermediate Value theorem, Properties of continuous functionsWeek 5:Differentiation, Rolle's Theorem, Mean Value theoremHigher derivatives Taylor theoremWeek 6:Curve tracing, Applications of derivativesWeek 7:Integrations, Week 8:Applications of Integration
Taught by
Prof. Parasar Mohanty